Vortex-lattice pinning in two-component Bose-Einstein condensates

We investigate the vortex-lattice structure for single- and two-component Bose-Einstein condensates in the presence of an optical lattice, which acts as a pinning potential for the vortices. The problem is considered in the mean-field quantum-Hall regime, which is reached when the rotation frequency $\Omega$ of the condensate in a radially symmetric trap approaches the (radial) trapping frequency $\omega$ and the interactions between the atoms are weak. We determine the vortex-lattice phase diagram as a function of optical-lattice strength and geometry. In the limit of strong pinning the vortices are always pinned at the maxima of the optical-lattice potential, similar to the slow-rotation case. At intermediate pinning strength, however, due to the competition between interactions and pinning energy, a structure arises for the two-component case where the vortices are pinned on lines of minimal potential

Pinning and collective modes of a vortex lattice in a Bose-Einstein condensate

We consider the ground state of vortices in a rotating Bose-Einstein condensate that is loaded in a corotating two-dimensional optical lattice. Due to the competition between vortex interactions and their potential energy, the vortices arrange themselves in various patterns, depending on the strength of the optical potential and the vortex density. We outline a method to determine the phase diagram for arbitrary vortex filling factor. Using this method, we discuss several filling factors explicitly. For increasing strength of the optical lattice, the system exhibits a transition from the unpinned hexagonal lattice to a lattice structure where all the vortices are pinned by the optical lattice. The geometry of this fully pinned vortex lattice depends on the filling factor and is either square or triangular. For some filling factors there is an intermediate half-pinned phase where only half of the vortices is pinned. We also consider the case of a two-component Bose-Einstein condensate, where the possible coexistence of the above-mentioned phases further enriches the phase diagram. In addition, we calculate the dispersion of the low-lying collective modes of the vortex lattice and find that, depending on the structure of the ground state, they can be gapped or gapless. Moreover, in the half-pinned and fully pinned phases, the collective mode dispersion is anisotropic. Possible experiments to probe the collective mode spectrum, and in particular the gap, are suggested.Comment: 29 pages, 4 figures, changes in section

NMR Experiments on Rotating Superfluid 3He-A : Evidence for Vorticity

Experiments on rotating superfluid 3He-A in an open cylindrical geometry show a change in the NMR line shape as a result of rotation: The amplitude of the peak decreases in proportion to f(T)g(Ω), where Ω is the angular velocity of rotation; at the same time the line broadens. Near Tc, f(T) is a linear function of 1−T/Tc. At small velocities g(Ω)∝Ω. These observations are consistent with the existence of vortices in rotating 3He-A.Peer reviewe

Transitions between turbulent and laminar superfluid vorticity states in the outer core of a neutron star

We investigate the global transition from a turbulent state of superfluid vorticity to a laminar state, and vice versa, in the outer core of a neutron star. By solving numerically the hydrodynamic Hall-Vinen-Bekarevich-Khalatnikov equations for a rotating superfluid in a differentially rotating spherical shell, we find that the meridional counterflow driven by Ekman pumping exceeds the Donnelly-Glaberson threshold throughout most of the outer core, exciting unstable Kelvin waves which disrupt the rectilinear vortex array, creating a vortex tangle. In the turbulent state, the torque exerted on the crust oscillates, and the crust-core coupling is weaker than in the laminar state. This leads to a new scenario for the rotational glitches observed in radio pulsars: a vortex tangle is sustained in the differentially rotating outer core by the meridional counterflow, a sudden spin-up event brings the crust and core into corotation, the vortex tangle relaxes back to a rectilinear vortex array, then the crust spins down electromagnetically until enough meridional counterflow builds up to reform a vortex tangle. The turbulent-laminar transition can occur uniformly or in patches; the associated time-scales are estimated from vortex filament theory. We calculate numerically the global structure of the flow with and without an inviscid superfluid component, for Hall-Vinen and Gorter-Mellink forms of the mutual friction. We also calculate the post-glitch evolution of the angular velocity of the crust and its time derivative, and compare the results with radio pulse timing data, predicting a correlation between glitch activity and Reynolds number.Comment: (1) School of Physics, University of Melbourne, Parkville, VIC 3010, Australia. (2) Departamento de Fisica, Escuela de Ciencias,Universidad de Oriente, Cumana, Venezuela, (3) Department of Mechanical and Manufacturing Engineering, University of Melbourne, Parkville, VIC 3010, Australia. Accepted for publication in The Astrophysical Journal. 30 pages, 9 figures (in jpg format